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JOURNAL OF PROPULSION AND POWER
Vol. 28, No. 4, July–August 2012
Technical Notes
Fluidic Thrust-Vector Control
of Supersonic Jet Using Coﬂow
Injection
thrust-vector control (FTVC) technique, which offers several
potential advantages over mechanical approaches: 1) no moving
parts interacting with the primary jet, 2) reduced weight and better
reliability, 3) improved stealth/low observability, 4) simplicity and
relatively low cost. Because of these advantages, there is currently
considerable interest in this type of system. A variety of approaches
to FTVC design, including coﬂows and counterﬂows, shock
methods, throat skewing, and dual-throat techniques have been
considered. Both the coﬂow and counterﬂow injection techniques are
based on the Coanda effect (an incident jet tends to remain attached to
a nearby surface) [4–10]. In the shock-injection TVC method
[11,12], an oblique shock is formed in the divergent nozzle to turn the
primary resulting from a secondary ﬂow into the primary jet at the
divergent nozzle wall. This method is characterized by large nozzleexpansion-area ratios and large thrust losses. The ﬂuidic throatskewing technique features symmetric injection for jet-area control
and asymmetric injection to skew the sonic plane for thrust-vector
control [13]. The dual-throat concept involves a convergent–
divergent–convergent nozzle [14–17]. A nonzero thrust-vector angle
is generated with ﬂuidic injection at the upstream throat that controls
separation and maximizes pressure difference in the recessed cavity
created between the two geometric minimum areas. The geometry is
intended to enhance the thrust-vectoring capability by manipulating
ﬂow separation in the recessed cavity. Indeed, ﬂuidic control is a very
appealing method of producing vectored thrust. Unfortunately, it is
apparent that ﬂuidic control is not without its difﬁculties, the most
serious of which is the hysteretic nature of these devices, which can
give rise to the attachment of the jet to the nozzle surfaces and thus
loss of control [18,19]. The technique of interest in the present
research is a coﬂow method based on the Coanda effect. This method
minimizes momentum loss in the jet because the control-ﬂow
injection direction is the same as that of the main jet. For this study, a
numerical simulation was performed and the results were compared
with steady-state experimental data to understand the effect of major
operating parameters, including the pressure ratio of the main and
control nozzles as well as the development of a shock behind the
control nozzle exit.
Jun-Young Heo∗ and Hong-Gye Sung†
Korea Aerospace University,
Goyang 412-791, Republic of Korea
DOI: 10.2514/1.B34266
Nomenclature
d
E
Fa
Fv
h
Pa
Pc
Pm
p
PR
qj
t
u
x
y
d
ij
ij
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
diameter of main nozzle exit
speciﬁc total energy
axial thrust
vertical thrust
speciﬁc enthalpy
atmospheric pressure
control-ﬂow total pressure
main-ﬂow total pressure
static pressure
pressure ratio of control ﬂow to main ﬂow
speciﬁc heat ﬂux
time
velocity
spatial coordinate
dimensionless wall distance
thrust deﬂection angle
Kronecker delta
density
viscous stress tensor
Superscripts
~
00
=
=
=
time average
Favre average
ﬂuctuation associated with mass-weighted mean
II. Numerical Method
The Favre-averaged governing equations based on the conservation of mass, momentum, and energy for a compressible ﬂow can be
written as
I. Introduction
T
HRUST-VECTOR control (TVC) systems tend to be
progressively implemented in modern aircraft and missiles to
improve the slow pitchover and limited maneuverability of the
aerodynamic control system [1–3]. A mechanical TVC system
moves a nozzle or deﬂectors to change the direction of a gas jet
exhausted from a nozzle. Although mechanical TVC systems are
widely applicable to conventional vehicles, they may be too heavy,
complex, and aerodynamically inefﬁcient for small vehicles and
applications in which multidirectional TVC systems are required.
One compact TVC alternative to mechanical TVC is the ﬂuidic
@ u~ j
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0
@xj
@t
(1)
ij @ij u00j u00i @ u~ i
@ u~ i @ u~ i u~ j p
@xj
@xj
@t
@t
Presented at the 45th AIAA/ASME/SAE/ASEE Joint Propulsion
Conference and Exhibit , Denver, CO, 2–5 August 2009; received 28
February 2011; revision received 7 January 2012; accepted for publication 11
January 2012. Copyright © 2012 by the American Institute of Aeronautics
and Astronautics, Inc. All rights reserved. Copies of this paper may be made
for personal or internal use, on condition that the copier pay the $10.00 percopy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive,
Danvers, MA 01923; include the code 0748-4658/12 and $10.00 in
correspondence with the CCC.
∗
Research Assistant, School of Aerospace and Mechanical Engineering.
†
Professor, School of Aerospace and Mechanical Engineering;
[email protected]. Associate Fellow AIAA.
ij @ij u00j u00i @ u~ i u~ j p
@xj
@xj
u~ j @u~ i ij h00 u00i @q j
@ E~ @ E~ p
@xj
@xj
@xj
@t
(2)
(3)
To account for the important features in high-speed ﬂow, the
combined model of compressible dissipation and pressure dilatation
proposed by Sarkar et al. [20,21] and the low-Reynolds-number k–"
model [22] was used in this study. The model was validated to be a
stable and accurate solver for the unsteady supersonic ﬂow, including
shock–boundary-layer interaction and ﬂow separation [23,24]. Over
858
J. PROPULSION, VOL. 28, NO. 4:
Fig. 1
Fig. 2
859
TECHNICAL NOTES
Experimental setup and schematic diagram of the FTVC nozzle.
Comparison of computational ﬂuid dynamics (CFD) results with schlieren images from the experiment.
the entire FTVC system, the ﬂowﬁelds are governed by a wide variety
of time scales, from stagnation in the main and control chambers to
supersonic ﬂow in the exhaust jet. Such a wide range of time scales
causes an unacceptable convergence problem. To overcome the
problem, a dual time-integration procedure designed for ﬂows at all
Mach numbers is applied. Dual time-stepping and lower–uppersymmetric Gauss–Seidel are applied for time integration, and the
control-volume method is used to integrate inviscid ﬂuxes represented by advection upstream-splitting method by pressure-based
weight functions and monotone upstream-centered schemes for
conservation laws and viscous ﬂuxes by central difference. The code
is parallelized using a message-passing-interface library to accelerate
the calculation.
III. Model Description
A schematic and a close-up view of the FTVC nozzle are shown in
Fig. 1. The secondary nozzles are positioned above and below the
primary nozzle. The primary nozzle was designed for isentropically
expanded ﬂow at Mach 2.0, corresponding to a Reynolds number of
1:2 106 at the exit plane, based on the height of the main nozzle
exit. In this study, the two divergent ﬂaps were ﬁxed at an angle of
10 deg.
IV.
In Fig. 3, the deﬂection angle of the jet increases with the ratio of
control-ﬂow total pressure to main-jet total pressure for pressure
ratios above 0.4. For pressure ratios between 0.1 and 0.4, the
maximum deﬂection angle increases linearly:
d;max 28:97 PR 1:60;
0:1 < PR < 0:4
(4)
The jet-deﬂection angle reaches a maximum value of about 10 deg,
which appears to be close to the angle of the nozzle’s divergent
section wall. This angle represents a hard maximum value imposed
by the geometry not by aerodynamics.
Figure 4 shows the ﬂow structure near the nozzle exit as the
control-ﬂow pressure increases and the jet pressure is kept constant.
The deﬂection angle of the jet gradually increases as injection control
pressure increases to 150 kPa, and then the deﬂection angle remains
constant at a control pressure of 200 kPa. Before the jet-deﬂection
angle reaches its maximum, the control ﬂow appears to be very
smooth. At Pc 200 kPa, shock waves are generated in the controlﬂow region, as shown in Fig. 4d, and the shock waves and nozzle
walls increase pressure. Especially, the presence of the shock waves
Results
A series of numerical and experimental tests were conducted. The
total pressure of the main jet was varied from 300 to 1000 kPa; the
pressure range of the overexpanded jet was from 300 to 600 kPa and
that of the underexpanded jet was from 790 to 1000 kPa. The total
pressure of the control ﬂow was varied from 120 to 250 kPa to
investigate the inﬂuence of control-ﬂow pressure on jet deﬂection.
Figure 2 shows the jet deﬂection from the nozzle axis at jet total
pressures of 300, 600, and 790 kPa with control-ﬂow pressures of
150 and 200 kPa. By visual comparison in Fig. 2, the numerically
determined ﬂow structures and deﬂection angles are similar to the
angles measured in the schlieren images from the experimental
results.
Fig. 3
Jet-deﬂection angle vs pressure ratio of control ﬂow to jet ﬂow.
860
J. PROPULSION, VOL. 28, NO. 4:
TECHNICAL NOTES
Fig. 4 Details of ﬂow structure near the control-ﬂow nozzle exit;
Pm 300 kPa.
prevents the jet from deﬂecting further due to reduce the pressure
difference between the walls (top and bottom). The deﬂection force
was generated by the pressure difference. However, the shock waves
lead to accelerate the pressure recovery at the jet-deﬂected side on
which the pressure difference reduces.
Figure 5 shows the pressure distribution along the top wall and a
schematic of the shock generation. The wavy shape of the pressure
distribution along the top nozzle wall is due to the presence of oblique
shock waves, which increase the pressure along the wall compared
with the Pc 120 kPa and Pc 150 kPa cases. The high pressure
with the wavy shape of pressure limits the deﬂection angle of jet ﬂow,
which in turn limits the control range of the FTVC using coﬂow
injection.
As shown in Fig. 6, axial thrust has a near-linear relation with the
main-jet pressure. Thrust increases as the control pressure increases
because the mass additions of control ﬂow in the axial direction.
Vertical thrust is generated as a result of jet deﬂection. Figure 7a
shows a schematic diagram of vertical thrust response to control jet
Fig. 5
Shock generation in the control-ﬂow nozzle exit.
Fig. 6 Axial thrust vs control-ﬂow pressure for various main-jet
pressures.
pressure: vertical thrust tends to remain constant, increase, and
decrease with increasing control pressure; these regimes may be
designated outside of control zone, control zone, and saturation zone,
respectively. Increasing control-ﬂow pressure in the control region,
the vertical thrust increases to some extent, but it decreases above a
certain pressure ratio in the saturated control zone. This is due to the
fact that, in the saturated zone, the control ﬂow not only causes ﬂow
deﬂection but also increases the axial force because of mass addition
to the main-jet ﬂow. As a result, the main ﬂow is separated from the
wall that caused a decrease in vertical thrust.
Figure 8 represents the thrust ratio of vertical thrust to axial thrust.
In general, thrust ratio increases as the PR increases; but, at 1000 kPa
for main and 200 kPa for control, the deﬂection force of jet does not
increase, and the controllability reaches the limit. In addition,
increase in Pc to 250 kPa causes normal shock between the primary
nozzle exit and the control wall, resulting in a decrease in Fv =Fa ,
shown in Figure 8. At 300 kpa for main, maximum Fv =Fa is
maximum at PR 0:4. Increasing PR causes a normal shock and
Fig. 7 Vertical thrust vs control-ﬂow pressure for different main-jet
pressures.
J. PROPULSION, VOL. 28, NO. 4:
TECHNICAL NOTES
[7]
[8]
[9]
[10]
[11]
Fig. 8 Thrust ratio vs pressure ratio for various main pressure
conditions.
[12]
loss of thrust as shown by decreasing Fv =Fa with increasing PR (see
Figs. 2a and 2b). To control the thrust vector effectively, the pressure
ratio should be set in the control zone; the proper range is from PR 0.1
to 0.3 in a main pressure range of between 450 kPa and 600 kPa.
[13]
V.
Conclusions
An investigation on operating parameters and dynamic characteristics of a FTVC system using a coﬂow control technique was studied
experimentally and numerically. The results of numerical
simulations were found to be fairly comparable with experimental
results. Jet-deﬂection angle and pressure distribution of the divergent
nozzle surface were measured as the ratio of control ﬂow to mainﬂow pressures. The maximum deﬂection angle was found to increase
linearly with the pressure ratio in a range of between 0.1 and 0.4. This
observation implies that the control efﬁciency will be maximized at
typical pressure ratios. Shocks appear in the control-ﬂow exit and
divergent wall as the control-ﬂow pressure increases, which limits
the jet-deﬂection angle. Axial thrust increases linearly with the
control pressure increase at different main-jet pressures. The
response to control-ﬂow pressure in terms of vertical thrust may be in
the control zone, outside of the control zone, or in the saturation zone.
Thus, the optimum PR should be found near the boundary
between the control zone and the saturation zone. That range is from
PR 0.1 to 0.3.
[14]
[15]
[16]
[17]
[18]
[19]
Acknowledgments
This study was partially supported by the Korea Research
Foundation in 2008 (KRF 2008-331-D00104), and the authors
would like to thank the Hanwha Corporation for partial funding
through a research consortium.
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C. Segal
Associate Editor